Re: LOGO-L> Arcs once again

[George Mills <mills@softronix.com>]

By definition I don't think either what you or I posted
is a hilbert curve. By definition an "ARC" based curve that
fills the space at its limit may be impossible.

Note also I think that the "High Orders" of the curves
should also be "ARC'd". That is each "level" should
form an ARC not just the lowest level.

Regardless though it can produce some interesting
art work.

I don't always know the answers to my suggestions :-)

Olga Tuzova wrote:
> 
> George,
> 
> As always, I'm feeling as if I'm trying to catch up the running away
> train. May be, it's just the time difference. :-)
> 
> > Date:          Wed, 06 May 1998 14:59:57 -0400
> > From:          George Mills <mills@softronix.com>
> > To:            Olga Tuzova <olgatu@ort.spb.ru>
> > Cc:            logo-l@gsn.org, cpthook@global2000.net
> > Subject:       Re: LOGO-L> Arcs once again
> > Reply-to:      George Mills <mills@softronix.com>
> 
> > Sorry Olga, I could not resist. Here is a a true Hilbert "Curve".
> >
> > Note, that all I did was take someones Hilbert Curve
> > http://www.xylem.demon.co.uk/hilbert.htm
> > and replace FD with FDA (Forward Arc).
> 
> It's a good challenge.
> I'm not well familiar with space filling curves and I'd rather go to
> the library and read something on this question, but as I haven't
> done this yet, I'm putting there the questions, for which I can't
> find answers.
> 
> The space filling curves I've seen before could fill a square and any
> iteration of the curve never leaves it. To fill a square I may just
> increase the level of iteration and don't have to change a size
> parameter.
> It looks like this Hilbert curve sooner or later will cross the
> boundaries of any large square. Is it so?
> 
> Apparently, there are characteristics for the curves  which allow to
> conclude whether the curve is space filling or not. I don't know
> them. Looking through the web sites I found some images which are
> considered to be iterations for space filling curves without proofs.
> Nevertheless they look fine and I tried to design Logo codes for
> one of them (http://www.math.utk.edu/~morwen/fill.html ).
> 
> I hope, they describe the curve perfectly and I took it for granted
> that it's space filling.
> 
> And, of course, I couldn't resist the temptation to make a "convex"
> version of it. Though, in this case, I'm afraid, the curve is loosing
> it's property to fill the space. In the attachment, if it isn't lost,
> there are iterations of the "straight" (red) and "convex" (blue)
> curves.
> 
> Regards,
> Olga.
> -----------------------------------------
> to filling.curve :size :level :p
> if :level<1 [fd :size rt :p*90 fd :size stop]
> filling.curve :size/2 :level-1 -:p rt :p*90
> filling.curve :size/2 :level-1 :p  lt :p*90
> filling.curve :size/2 :level-1 :p  rt :p*90
> filling.curve :size/2 :level-1 -:p
> end
> 
> to convex.filling.curve :size :level :p
> if :level<1 [fda :size rt :p*90 fda :size stop]
> convex.filling.curve :size/2 :level-1 -:p rt :p*90
> convex.filling.curve :size/2 :level-1 :p  lt :p*90
> convex.filling.curve :size/2 :level-1 :p  rt :p*90
> convex.filling.curve :size/2 :level-1 -:p
> end
> 
> to fda :size
> lt 90
> arc2 180 :size/2
> lt 90
> end
> -----------------------------------------
> 
> >
> > to fda :dist
> > lt 90
> > arc2 180 :dist/2
> > lt 90
> > end
> >
> > to go
> > cs
> > pu
> > setxy 250 -250
> > pd
> > hilbert 20 5 45
> > end
> >
> > to hilbert :size :level :parity
> > if :level > 0 ~
> >   [
> >   lt :parity*90 hilbert :size :level-1 :parity*-1
> >   fda :size
> >   rt :parity*90 hilbert :size :level-1 :parity
> >   fda :size
> >   hilbert :size :level-1 :parity rt :parity*90
> >   fda :size
> >   hilbert :size :level-1 :parity*-1 lt :parity*90
> >   ]
> > end
> >
> > --

-- 
===============================================================
George Mills
email: mills@softronix.com
http://www.softronix.com
The www page contains some very powerful educational software.
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